GENEVA — The United Nations mediator for Syria, Lakhdar Brahimi, wrapped up the second round of peace talks here on Saturday without breaking a longstanding deadlock or setting a date for a third round, and urged the parties to think seriously about their commitment to the negotiations.

Mr. Brahimi said the talks had broken down primarily because the Syrian government balked at his suggestion that the negotiators discuss both sides’ top demands in the first two days of negotiations, rather than spending days on the government’s priorities.

“I am very, very sorry, and I apologize to the Syrian people,” Mr. Brahimi, an Algerian diplomat who has spent decades negotiating thorny conflicts, said after a last-ditch, 45-minute meeting with the two sides ended in disagreement. “I apologize to them that on these two rounds we haven’t helped them very much.”

The dispiriting finish called into question the future of the talks. Two weeklong rounds have produced no actual negotiations on resolving a conflict that has killed more than 135,000 people and driven 9.5 million from their homes, even though the talks are sponsored by Russia and the United States, which support opposing sides, and backed by dozens of other countries. The meetings have instead focused on what to discuss and how to do so.

“It’s not good for Syria that we come back for another round and fall in the same trap that we have been struggling with this week and most of the first round,” Mr. Brahimi said. “So I think it is better that every side goes back and reflect and take their responsibility: Do they want this process to take place or not? I will do the same.”

He said he would report to the United Nations secretary general, Ban Ki-moon, and push for a meeting with Mr. Ban, Secretary of State John Kerry and the Russian foreign minister, Sergey V. Lavrov. Some Western diplomats have suggested that Mr. Brahimi, 80, might be worried about harming his legacy by presiding over empty talks, and so might recommend ending them. But others pointed out that he was famous for his patience.

Both the government and the opposition said they would return if another round were called.

Western officials were quick to call for new pressure on the Syrian government. Minutes after Mr. Brahimi spoke, the British foreign secretary, William Hague, wrote in a Twitter message that the United Nations Security Council “must now act to address the humanitarian crisis urgently.” But Russia, the Syrian government’s most powerful backer, sees Western attempts to require access for aid workers as a pretext for military action, and has blocked previous Security Council measures on Syria.

Mr. Brahimi said the two sides had agreed that a third round of talks would address both the opposition’s top-priority issue (political transition) and the government’s (the ending of terrorism, which it says includes all armed opposition). But then, he said, the government rejected his proposal that the negotiators spend the first day on terrorism and the second on transition.

Both are contentious issues: the government recently placed all the opposition coalition members, even the civilians across the negotiating table, on a list of terrorists, and for the opposition, transition implies an end to the government of which its interlocutors are members.

Bashar al-Jaafari, the Syrian ambassador to the United Nations in New York and the government’s lead negotiator, said it would be impossible to resolve the issue of terrorism in one day and the government wanted to reach “a common vision” on the subject before moving on to others.

But Mr. Brahimi said he had made it “very clear” that both topics would take far more than one day, and that his aim was simply to ensure that the two sides at least began to discuss each other’s demands. He said he had told government negotiators that this would reassure the opposition, which is “very suspicious” of the government and believes that it does not want to discuss a transition at all.

“I hope that this time of reflection will lead the government side in particular to reassure the other side that when they speak of implementing the Geneva communiqué,” they mean that “the main objective” is a transitional governing body with full executive powers, Mr. Brahimi said, referring to the July 2012 document that is the basis for the talks.

“Ending violence, combating terrorism is extremely important, indispensable,” he said. “But I think that every side has to be convinced that, yes, we are going to implement all the elements in the communiqué.”

Each side blamed the other and its international backers for the lack of progress. “We are here to negotiate,” said Louay Safi, a spokesman for the opposition. “We have been disappointed completely, not only by the regime.”

Russian officials “have not prevailed over the regime that wants to stall,” Mr. Safi said, adding that Russia continued to supply the weapons the Syrian government is using to bombard rebel-held towns and neighborhoods.

Mr. Jaafari said recent comments by President Obama and members of his administration, who mentioned the possibility of greater efforts to help the opposition, meant American officials were “not committed” to the success of talks.

The Syrian government has long said that the first step toward ending the conflict must be the end of support for insurgent groups by the United States and allies, including Qatar and Saudi Arabia.

Mr. Jaafari said the government recognized that the opposition delegation could not single-handedly stop terrorism in Syria, because it does not control many of the insurgent groups. But, he added, officials want to hear that the opposition is committed to stopping it.

The opposition has condemned violence against civilians and pointed to its affiliated fighters’ recent battles against jihadist groups. But the crux of the dispute is the definition of terrorism.

In a sign of just how broadly the government defines terrorism, opposition delegates said Saturday that they had recently learned that the government had placed the names of everyone in their entire coalition on a “terrorist list” and seized their assets. Mr. Jaafari confirmed the news — which was posted on an opposition website last week — and said the decision was made before the talks began.

“Whoever refuses to fight terrorism is part of terrorism,” he said.

Ahmad Jakal, an opposition delegate, said, “They are negotiating with us, but they call us terrorists.” A pro-government analyst based in Damascus, the Syrian capital, who spoke anonymously in order to be more open, said the definition of terrorism was a “subject for negotiations.”

Both sides have legitimate points, the analyst said: The government is correct that a smooth political transition cannot occur amid continuing violence, and the opposition is correct that the violence cannot end unless political demands are addressed. Because of this, he said, speaking about both terrorism and transition makes sense.

But he added that the government delegation would have a hard time persuading its base, including the powerful security services and military, to talk about dismantling or reshaping the government of President Bashar al-Assad when they believe they are gaining on the ground.

Members of the opposition delegation said they hoped that the talks in Geneva had highlighted the government’s inflexibility and might prompt a stronger international response — perhaps pressure from Russia, increased military aid for the opposition, Security Council resolutions, or even a no-fly zone to stop government airstrikes.

As the delegates prepared to leave on Saturday, Mr. Jaafari turned prickly when asked by a reporter what would entice Mr. Assad’s team back to the table.

“Your nice face,” he shot back.

A version of this article appears in print on , on Page A18 of the New York edition with the headline: After Second Round of Syria Talks, No Agreement Even on How to Negotiate. Order Reprints | Today’s Paper | Subscribe